2026-04-13T05:43:20Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1658852026-02-07T11:54:54Zcom_2072_1033col_2072_452950

urn:hdl:2117/165885 Stable s-minimal cones in R 3 are flat for s ~ 1 Cabré Vilagut, Xavier Cinti, Eleonora Serra, Joaquim Àrees temàtiques de la UPC::Matemàtiques i estadística Differential equations Equacions integro-diferencials We prove that half spaces are the only stable nonlocal s-minimal cones in R3, for s¿(0,1) sufficiently close to 1. This is the first classification result of stable s-minimal cones in dimension higher than two. Its proof cannot rely on a compactness argument perturbing from s=1. In fact, our proof gives a quantifiable value for the required closeness of s to 1. We use the geometric formula for the second variation of the fractional s-perimeter, which involves a squared nonlocal second fundamental form, as well as the recent BV estimates for stable nonlocal minimal sets Peer Reviewed Postprint (author's final draft) 2019-01-01 Article https://www.degruyter.com/view/j/crll.ahead-of-print/crelle-2019-0005/crelle-2019-0005.xml http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain